Embedded Software for SoC - Grupo de Mecatrônica EESC/USP

264 Chapter 20
3.1. Petri net fundamentals
A Petri net, PN is a tuple (P, T, F, where P and T are sets of nodes of
place or transition type respectively [7]. F is a function of
to the set of non-negative integers. A marking M is a function of P to the set
of non-negative integers. A number of tokens of p in M, where p is a place
of the net, equals to the value of the function M for p, that is, M[p]. If
M[p] > 0 the place is said to be marked. Intuitively, the marking values of all
the places of the net constitute the system state.
A PN can be represented as a bipartite directed graph, so that in case the
function F(u, v) is positive, there will exist an edge [u, v] between such graph
nodes u and v. The value F(u, v) is the edge weight. A transition t is enabled
in a marking M if
In this case, the transition can be
fired in the marking M, yielding a new marking given by
A marking is reachable from the initial marking if there exists a
sequence of transitions that can be sequentially fired from to produce
Such a sequence is said to be fireable from The set of markings reachable
from is denoted The reachability graph of a PN is a directed
graph in which is a set of nodes and each edge corresponds
to a PN transition, t, such that the firing of t from marking M gives
A transition t is called source transition if
A pair of
non source transitions and are in equal conflict if
An equal conflict set, ECS is a group of transitions that are in equal conflict.
A place is a choice place if it has more than one successor transition. If
all the successor transitions of a choice place belong to the same ECS, the
place is called equal choice place. A PN is Equal Choice if all the choice
places are equal.
A choice place is called unique choice if in every marking of that
place cannot have more than one enabled successor transition. A uniquechoice
Petri net, UCPN, is one in which all the choice places are either unique
or equal. The PNs obtained after compiling our high-level specification present
unique-choice ports.
3.2. Conditions for valid schedules
A schedule for a given PN is a directed graph where each node represents a
marking of the PN and each edge joining two nodes stands for the firing of
an enabled transition that leads from one marking to another. A valid schedule
has five properties. First, there is a unique root node, corresponding to the
starting marking. Second, for every marking node v, the set of edges that
start from v must correspond to the transitions of an enabled ECS. If this
ECS is a set of source transitions, v is called an await node. Third, the nodes
v and w linked by an edge t are such that the marking w is obtained after firing